"There's been a big feeling among a number of reef managers worldwide that perhaps their actions locally are futile," says Mumby. "I speak to people frequently who say 'Gosh, why are we doing this if it's all going to go with climate change?'

"Yes we need to act globally on climate change but local management is far from futile. It's absolutely essential."

Hundreds of millions of people depend on coral reefs for their daily food and livelihoods but reefs are under threat from climate change.

Warming seas are expected to lead to more severe coral bleaching and a rise in water temperatures of just 1 or 2 degrees above normal is enough to kill vast areas of reef.

The ability of reefs to bounce back from such events is affected by factors such as overfishing and pollution.

While Australia's reefs are still fairly healthy, Mumby says those in the Caribbean have shown quite profound declines in health over the last few decades.

"On a good reef you would expect to see at least half of the reef covered in living coral. These days it's not uncommon to go to a reef in the Caribbean and perhaps only 15 per cent of the reef is living coral," he says.

Using data from long-suffering coral reefs in the Caribbean, which are regarded as a 'test bed' for the world's reefs, Mumby and colleagues have developed a new model to predict the effect of local action on overfishing and pollution, and global action on greenhouse emissions, on coral reefs.

As well as simulating how corals will grow given expected climate change and ocean acidification, the model is the first to incorporate factors that erode the calcium carbonate backbone of reefs.

This enabled the researchers to calculate the "carbonate budget" for a typical Caribbean reef.

In a positive carbonate budget, the amount of calcium carbonate produced by corals outweighs the amount of calcium carbonate that is eroded away. In a negative carbonate budget, erosion wins and the reef shrinks.

"You've got a balance between the things that are building the reef and things that are eroding it away," says Mumby.

"What you really want is for your budget to be positive so the reef is continuing to grow and keep pace with sea level rise and so forth."

Humans and reef erosion

The loss of calcium carbonate is caused by a range of things from parrotfish nibbling the reef to sponges boring into the reef for shelter. While these are natural processes, human activity can make matters worse, says Mumby.

"Once you start adding humans into the equation you end up with levels of erosion that are not natural."

For example, he says, nutrient run-off on to the reef increases plankton, which increases the number of animals feeding on the reef, which in turn increases erosion. Overfishing of parrotfish, which feed on seaweed, also leads to more seaweed, which smothers baby coral and prevents recolonisation.

"Reefs are being hit with a double whammy. On the one hand the things that build them are becoming fewer and fewer and the things that erode them are getting more and more abundant. So we're shifting the balance," says Mumby.

While global action on greenhouse gases can help reduce coral bleaching, Mumby says overfishing and pollution must be dealt with locally. He says the new model shows in order to maintain a positive carbonate budget for reefs towards the end of this century, both actions are needed.

"If we only have one or the other then reefs will very likely shift into erosion towards the end of the century."

Even if the IPCC's most optimistic scenario for greenhouse emission reduction is followed, Mumby says coral reefs will still be under threat unless local action is taken.

"If we don't take care of them locally then even all this action climate change is not going to be enough."

If nothing is done about greenhouse emissions, Mumby and colleagues calculate that local action on pollution and overfishing can delay a negative reef carbonate budget for at least 10 years.

Mumby says that one uncertainty in the model is that the "jury is still out" on the degree to which corals will be able to adapt to global warming.